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DK13: Multivariate Symbolic Asymptotics

Supervisor: Prof. Manuel Kauers

The goal of this project is the development of computer algebra algorithms for obtaining asymptotic information of functions and sequences in several variables. Solving problems in discrete mathematics often requires to deal with symbolic sums, generating functions, recurrence equations, and asymptotic estimates. In the case of a single variable, computer algebra tools for working with all these four concepts are available since long. Recent research has focused on algorithms applicable to objects depending on several variables. Most of this research concerned only symbolic sums, generating functions, and recurrence equations, while almost no work has been done so far on computing asymptotic estimates in the multivariate case. The goal of the research done in DK13 is to help closing this gap. There are various interesting questions in this area which could be addressed in a PhD thesis, combining pure algorithm development with concrete applications connecting to other projects of the DK.